Conformal structure of massless scalar amplitudes beyond tree level

  • Nabamita Banerjee
  • Shamik Banerjee
  • Sayali Atul Bhatkar
  • Sachin Jain
Open Access
Regular Article - Theoretical Physics


We show that the one-loop on-shell four-point scattering amplitude of massless ϕ4 scalar field theory in 4D Minkowski space time, when Mellin transformed to the Celestial sphere at infinity, transforms covariantly under the global conformal group (SL(2, ℂ)) on the sphere. The unitarity of the four-point scalar amplitudes is recast into this Mellin basis. We show that the same conformal structure also appears for the two-loop Mellin amplitude. Finally we comment on some universal structure for all loop four-point Mellin amplitudes specific to this theory.


Conformal Field Theory Global Symmetries Scattering Amplitudes 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Nabamita Banerjee
    • 1
  • Shamik Banerjee
    • 2
  • Sayali Atul Bhatkar
    • 1
  • Sachin Jain
    • 1
  1. 1.Indian Institute of Science Education and ResearchPuneIndia
  2. 2.Institute of PhysicsBhubaneswarIndia

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